document.write( "Question 1139263: 3.
\n" ); document.write( "Windies Bats produces two models of cricket bats,the Layle and the Gara. They are produced on two separate assembly lines. Producing a Layle requires 2 hours on Line I and 1 hour on Line II, while producing a Gara requires 1 hour on Line I and 3 hours on Line II. Sixty hours available for production on Line I and forty on Line II. The unit profit on the Layle is $150 while that on the Gara is $200.
\n" ); document.write( "a. Write a model to describe the information presented.\r
\n" ); document.write( "\n" ); document.write( "The diagram above shows the solution set shaded purple. Matching it to the information given:
\n" ); document.write( "b. Determine how many of each model maximizes the profit?
\n" ); document.write( "c. What is the maximum possible profit? \n" ); document.write( "

Algebra.Com's Answer #757090 by Edwin McCravy(20056) $\"\"$ $\"About$

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3. Windies Bats produces two models of cricket bats,the Layle and the Gara. They\r\n" );
document.write( "are produced on two separate assembly lines. Producing a Layle requires 2 hours\r\n" );
document.write( "on Line I and 1 hour on Line II, while producing a Gara requires 1 hour on Line\r\n" );
document.write( "I and 3 hours on Line II. Sixty hours available for production on Line I and\r\n" );
document.write( "forty on Line II. The unit profit on the Layle is $150 while that on the Gara is\r\n" );
document.write( "$200.\r\n" );
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document.write( ".....how many of each model maximizes the profit?\r\n" );
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document.write( "Let x = the number of Layles and y = the number of Garas.\r\n" );
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document.write( "Producing a Layle requires 2 hours on Line I....., while producing a Gara\r\n" );
document.write( "requires 1 hour on Line I..... Sixty hours available for production on Line\r\n" );
document.write( "I.....\r\n" );
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document.write( "  (the line I inequality)\r\n" );
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document.write( "Producing a Layle requires.....1 hour on Line II, while producing a Gara\r\n" );
document.write( "requires....3 hours on Line II.  …..forty (hours available for production) on\r\n" );
document.write( "Line II.\r\n" );
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document.write( "   (the line II inequality)\r\n" );
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document.write( "The unit profit on the Layle is $150 while that on the Gara is $200.\r\n" );
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document.write( "a. Write a model to describe the information presented.\r\n" );
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document.write( "Maximize \r\n" );
document.write( "subject to constraints\r\n" );
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document.write( "The last two constraints tell us that the feasible region is\r\n" );
document.write( "in the upper right hand part of the graph, QI\r\n" );
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document.write( "We draw the boundary line 2x+y=60, which has intercepts (30,0) and (0,60)\r\n" );
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document.write( "We draw the boundary line x+3y=40, which has intercepts (40,0) and (0,13 1/3)\r\n" );
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document.write( "We solve the system of the boundary lines by substitution or elimination\r\n" );
document.write( "to find any points where they intersect which are vertices of the feasible region:\r\n" );
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document.write( "We get their point of intersection as (x,y) = (28,4)\r\n" );
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document.write( "We test the objective function at each of the four corner points:\r\n" );
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document.write( "(0,0)  P = 150x+200y = 150(0)+200(0) = 0+0 = 0\r\n" );
document.write( "(30,0)  P = 150x+200y = 150(30)+200(0) = 4500+0 = 4500\r\n" );
document.write( "(28,4)  P = 150x+200y = 150(28)+200(4) = 4200+890 = 5000\r\n" );
document.write( "(0,0)  P = 150x+200y = 150(0)+200(4/30) = 0+8000/3 = 2666.67\r\n" );
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document.write( "So they should make 28 Layles and 4 Garas for a maximum profit of $5000\r\n" );
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document.write( "Edwin

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